Suppose that x has an exponential distribution with $\theta = 2 . \text { Find } P ( x

Name: Suppose that x has an exponential distribution with $\theta = 2 . \text { Find } P ( x < 1.5 )$ A) 0.527633 B) 0.472367 C) 0.736403 D) 0.263597
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Question

Suppose that x has an exponential distribution with $\theta = 2 . \text { Find } P ( x < 1.5 )$
A) 0.527633
B) 0.472367
C) 0.736403
D) 0.263597

Quizplus · Accepted Answer

The cumulative distribution function (CDF) for an exponential distribution is $ P(x < a) = 1 - e^{-a/\theta} $. Substituting $ a = 1.5 $ and $ \theta = 2 $, we get $ P(x < 1.5) = 1 - e^{-1.5/2} = 1 - e^{-0.75} \approx 0.527633 $.

Suppose That X Has an Exponential Distribution With θ=2. Find P(x<1.5)\theta = 2 . \text { Find } P ( x < 1.5 )θ=2. Find P(x<1.5)

Suppose That X Has an Exponential Distribution With $\theta = 2 . \text { Find } P ( x < 1.5 )$